We were spending a week together, just the two of us, in Copenhagen, a city heralded as a Shangri-la for cyclists. Spend a few days there and you’ll watch thousands of beautiful, straight-spined Danes whooshing by you on their two-wheelers — often with toddlers riding shotgun in wooden seats fixed to the front.

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Toby, a 12-year-old Yankees fan who counters my sedentary inclinations with the bottomless energy of a triathlete, wanted to experience Copenhagen as locals do. It was pointless to resist: we found ourselves renting bikes from a helpful man named Mustapha at one of the shops on Gothersgade. Our picks seemed to echo our mentalities: thick-tired and sturdy, Toby’s model could’ve withstood a motocross race, whereas mine — basket-prowed and quaint — looked like it’d been owned by Mary Poppins.

After handing over my license as collateral (a common practice for renting bikes), we set out to see the city of Hans Christian Andersen from its most charming vantage point. Though I’d traveled to Copenhagen many times to report on permutations of the New Nordic culinary scene, I’d somehow dodged its most popular mode of transportation.

In fact, I had avoided many of the city’s most obvious delights. In focusing so squarely on seeking out the trailblazing and new, I’d overlooked the old and iconic. As Toby taught me, sidestepping the established stuff in Copenhagen can be a big mistake.

One of the most obvious examples is visible (and audible) from all over the city. Look up and listen for the screams: the Star Flyer rises from the middle of the Tivoli Gardens amusement park and carries people around in speedy, delirious whirls. Toby wanted to do that, too, and so we did — though I nearly parted ways with breakfast as a result. We rode the bumper cars and the Rutschebanen, a wooden roller coaster that dates back to 1914.

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How did I think, in my five preceding visits, that I could grasp the spirit of Copenhagen without spending a day at the 19th-century playland that Walt Disney went to for inspiration to try his hand at a similar thing in southern California? Our bicycle outing felt like such a success that we did it twice. We went in search of the Little Mermaid statue and wound up instead dodging tourists in Nyhavn. Then we skirted the edge of Freetown Christiania, the city’s unruly enclave of tree-painted houses and pot smoke. Toby declined to venture in; maybe we’ll try again in a few years.

And in all of my quests for unfamiliar flavors in the Danish capital, how had I skipped over the classics? Toby wanted shrimp, and I craved herring, which sent us to Restaurant Palægade and Told & Snaps, two Copenhagen stalwarts that uphold the standards of smørrebrød by paying close attention to the quality of each ingredient.

Our last dinner in Denmark came together at Marchal, inside the gracious and grand Hotel d’Angleterre, where we feasted on gougères and caviar, and where chef Andreas Bagh gave my son a spin at a gleaming French duck press. The tool was more than a century old, we learned. But while I watched Toby straining to turn the ancient wheel, it dawned on me: for my son, many of the things I consider quintessential are all brand-new.